At any instant of time t, the displacement of any particle is given by 2t – 1 (SI unit) under the influence of force of 5 N. The value of instantaneous power is (in SI unit):

To find the instantaneous power, we can use the relationship between force, velocity, and power.

First, let's identify the given quantities from the problem:
The displacement of the particle, $x=2t-1$ (in meters)
The constant force acting on the particle, $F=5$ N

The velocity $v$ of the particle is the rate of change of displacement with respect to time $t$. We can find $v$ by differentiating the displacement function:
$v=\frac{dx}{dt}=\frac{d}{dt}(2t-1)$
$v=2$ m/s

The instantaneous power $P$ is defined as the dot product of the force and the velocity vectors. Since the motion is in one dimension, it is simply the product of the force and velocity:
$P=F·v$

Substitute the given values of force and velocity into the formula:
$P=5·2=10$ W

Therefore, the value of the instantaneous power is 10 in SI units (Watts).